Active photonic devices with enhanced Pockels effect via isotope substitution

ABSTRACT

A waveguide structure includes a substrate, a waveguide core coupled to the substrate and including a first material characterized by a first index of refraction, and an isotope-enhanced cladding layer at least partially surrounding the waveguide core and including a second material characterized by a second index of refraction less than the first index of refraction and an isotope-enhanced Pockels effect.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application claims the benefit of priority to U.S. ProvisionalPatent Application No. 62/864,975, filed on Jun. 21, 2019, entitled“Active Photonic Devices with Enhanced Pockels Effect via IsotopeSubstitution,” the disclosure of which is hereby incorporated byreference in its entirety for all purposes.

BACKGROUND OF THE INVENTION

Electro-optic (EO) modulators and switches have been used in opticalfields. Some EO modulators utilize free-carrier electro-refraction,free-carrier electro-absorption, or the DC Kerr effect to modify opticalproperties during operation, for example, to change the phase of lightpropagating through the EO modulator or switch. As an example, opticalphase modulators can be used in integrated optics systems, waveguidestructures, and integrated optoelectronics.

Despite the progress made in the field of EO modulators and switches,there is a need in the art for improved methods and systems related toEO modulators and switches.

SUMMARY OF THE INVENTION

Embodiments of the present invention generally relate to photonicdevices. More particularly, embodiments of the present invention relateto active photonic devices utilized as components of optical modulatorsand optical switches. In a particular embodiment, active photonicdevices with low optical loss and reduced switching energies areprovided that include waveguide core or waveguide cladding materialscharacterized by a Pockels effect that is increased via isotopesubstitution. These materials characterized by an isotope-enhancedeffect can be utilized to improve modulation and/or switchingperformance. The present invention has applicability to a wide varietyof photonic and opto-electronic devices.

According to an embodiment of the present invention, a waveguidestructure is provided. The waveguide structure includes a substrate, awaveguide core coupled to the substrate and including a first materialcharacterized by a first index of refraction, and an isotope-enhancedcladding layer at least partially surrounding the waveguide core andincluding a second material characterized by a second index ofrefraction less than the first index of refraction and anisotope-enhanced Pockels effect.

According to another embodiment of the present invention, an opticalswitch structure is provided. The optical switch structure includes asubstrate and a waveguide structure coupled to the substrate. Theoptical switch structure also includes a set of electrodes positionedadjacent the waveguide structure. The set of electrodes are configuredto establish an applied electric field having a component oriented alonga lateral direction. The waveguide structure includes a waveguide coreconfigured to support a guided mode and propagating along a longitudinaldirection orthogonal to the lateral direction and including a firstmaterial characterized by a first index of refraction. The waveguidestructure also includes an isotope-enhanced waveguide cladding at leastpartially surrounding the waveguide core and including a second materialcharacterized by a second index of refraction less than the first indexof refraction and an isotope-enhanced Pockels effect higher than aPockels effect of the second material with constituent materials havingnaturally occurring isotope percentages.

According to a specific embodiment of the present invention, a waveguidestructure is provided. The waveguide structure includes a substrate anda waveguide core coupled to the substrate and including a first materialcharacterized by a first index of refraction and an isotope-enhancedPockels effect greater than a Pockels effect of the first material withconstituent materials having naturally occurring isotope percentages.The waveguide structure also includes a cladding layer at leastpartially surrounding the waveguide core and including a second materialcharacterized by a second index of refraction less than the first indexof refraction.

According to a particular embodiment of the present invention, asemiconductor structure is provided. The semiconductor structureincludes a silicon substrate structure and an isotope-enhanced layercoupled to the silicon substrate structure.

Numerous benefits are achieved by way of the present disclosure overconventional techniques. For example, embodiments of the presentinvention provide methods and systems that can utilize a reduced appliedbias to achieve a given electric field in a waveguide core or waveguidecladding, thereby reducing power consumption and increasing efficiency.Moreover, by increasing the Pockels effect of the materials used tomodulate the phase of light through changes in effective refractiveindex, embodiments of the present invention facilitate the use of lowervoltages and/or smaller devices. This in turn, enables lowerswitching/operating voltages and reduced optical absorption. These andother embodiments of the disclosure along with many of its advantagesand features are described in more detail in conjunction with the textbelow and attached figures.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a simplified schematic diagram illustrating an optical switchaccording to an embodiment of the present invention.

FIG. 2 is a simplified schematic diagram showing a top view of an activewaveguide region according to an embodiment of the present invention.

FIG. 3 is a simplified schematic diagram illustrating adielectric-waveguide-dielectric structure incorporating isotope-enhancedmaterials according to an embodiment of the present invention.

FIG. 4 is a simplified schematic diagram illustrating a p-n diodewaveguide structure incorporating isotope-enhanced cladding materialsaccording to an embodiment of the present invention.

FIG. 5 is a simplified schematic diagram illustrating a waveguidestructure incorporating isotope-enhanced cladding materials according toan embodiment of the present invention.

FIG. 6 is a simplified schematic diagram illustrating a p-n diodewaveguide structure incorporating a planar isotope-enhanced claddinglayer according to an embodiment of the present invention.

FIG. 7 is a simplified schematic diagram illustrating a buried waveguidestructure incorporating a planar isotope-enhanced cladding layeraccording to an embodiment of the present invention.

FIG. 8 is a simplified schematic diagram illustrating a buried waveguidestructure incorporating a planar isotope-enhanced cladding layeraccording to another embodiment of the present invention.

FIG. 9 is a simplified schematic diagram illustrating adielectric-waveguide-dielectric structure incorporating isotope-enhancedcladding materials according to an embodiment of the present invention.

FIGS. 10A-10C are simplified schematic diagrams illustrating fabricationof an isotope-enhanced semiconductor structure according to anembodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

Embodiments of the present invention relate to optical systems. Moreparticularly, embodiments of the present invention utilizeisotope-enhanced Pockels effect materials (i.e., high-χ⁽²⁾ materials) inoptical modulators and switches to reduce power consumption duringoperation. Merely by way of example, embodiments of the presentinvention are provided in the context of integrated optical systems thatinclude active optical devices, but the invention is not limited to thisexample and has wide applicability to a variety of optical andoptoelectronic systems.

According to some embodiments, the active photonic devices describedherein utilize the Pockels effect to implement modulation and/orswitching of optical signals. Thus, embodiments of the present inventionare applicable to both modulators, in which the transmitted light ismodulated either ON or OFF, or light is modulated with a partial changein transmission percentage, as well as optical switches, in which thetransmitted light is output on a first output (e.g., waveguide) or asecond output (e.g., waveguide) or an optical switch with more than twooutputs, as well as more than one input. Thus, embodiments of thepresent invention are applicable to a variety of designs including anM(input)×N(output) systems that utilize the methods, devices, andtechniques discussed herein.

FIG. 1 is a simplified schematic diagram illustrating an optical switchaccording to an embodiment of the present invention. Referring to FIG.1, switch 100 includes two inputs: Input 1 and Input 2 as well as twooutputs: Output 1 and Output 2. As an example, the inputs and outputs ofswitch 100 can be implemented as optical waveguides operable to supportsingle mode or multimode optical beams. As an example, switch 100 can beimplemented as a Mach-Zehnder interferometer integrated with a set of50/50 beam splitters 105 and 107, respectively. As illustrated in FIG.1, Input 1 and Input 2 are optically coupled to a first 50/50 beamsplitter 105, also referred to as a directional coupler, which receiveslight from the Input 1 or Input 2 and, through evanescent coupling inthe 50/50 beam splitter, directs 50% of the input light from Input 1into waveguide 110 and 50% of the input light from Input 1 intowaveguide 112. Concurrently, first 50/50 beam splitter 105 directs 50%of the input light from Input 2 into waveguide 110 and 50% of the inputlight from Input 2 into waveguide 112. Considering only input light fromInput 1, the input light is split evenly between waveguides 110 and 112.

Mach-Zehnder interferometer 120 includes phase adjustment section 122.Voltage V₀ can be applied across the waveguide in phase adjustmentsection 122 such that it can have an index of refraction in phaseadjustment section 122 that is controllably varied. Because light inwaveguides 110 and 112 is in-phase after propagation through the first50/50 beam splitter 105, phase adjustment in phase adjustment section122 can introduce a predetermined phase difference between the lightpropagating in waveguides 130 and 132. As will be evident to one ofskill in the art, the phase relationship between the light propagatingin waveguides 130 and 132 can result in output light being present atOutput 1 (e.g., light beams are in-phase) or Output 2 (e.g., light beamsare out of phase), thereby providing switch functionality as light isdirected to Output 1 or Output 2 as a function of the voltage V₀ appliedat the phase adjustments section 122. Although a single active arm isillustrated in FIG. 1, it will be appreciated that both arms of theMach-Zehnder interferometer can include phase adjustment sections.

As illustrated in FIG. 1, electro-optic switch technologies, incomparison to all-optical switch technologies, utilize the applicationof the electrical bias (e.g., V₀ in FIG. 1) across the active region ofthe switch to produce optical variation. The electric field and/orcurrent that results from application of this voltage bias results inchanges in one or more optical properties of the active region, such asthe index of refraction or absorbance. In addition to the powerdissipated by current flow (in the cases where a current results fromthe application of the bias voltage), energy is dissipated by thecreation of the electric field, which has an energy density of E²_(κ)/8π (cgs units), where E is the electric field and κ is thedielectric constant.

Although a Mach-Zehnder interferometer implementation is illustrated inFIG. 1, embodiments of the present invention are not limited to thisparticular switch architecture and other phase adjustment devices areincluded within the scope of the present invention, including ringresonator designs, Mach-Zehnder modulators, generalized Mach-Zehndermodulators, and the like. One of ordinary skill in the art wouldrecognize many variations, modifications, and alternatives.

The inventors have determined that because the energy density is higherin regions with a high dielectric constant, incorporation ofisotope-enhanced Pockels effect materials into the electro-optic switcharchitecture can reduce the overall power consumption of theelectro-optic switch since the dielectric tensor components scaleroughly linearly with the Pockels tensor coefficients. As a result, theenergy used to switch the electro-optic switch will generally scale asthe dielectric constant over the square of the effective Pockelscoefficient, thereby resulting in reduced power consumption as thePockels effect and the dielectric constant increase.

FIG. 2 is a simplified schematic diagram showing a top view of an activewaveguide region according to an embodiment of the present invention. InFIG. 2, metal electrodes 210 and 212 are positioned on either side ofwaveguide core 220, which is disposed between waveguide cladding regions222 and 224. In this implementation, the waveguide core 220 isfabricated using silicon and the waveguide cladding regions 222 and 224are fabricated using silicon dioxide. The dielectric constants of thematerials are represented by the κ values of 11.7 for Si and 3.9 forSiO₂. The thickness of the layers (i.e., d_(Si) and d_(ox)) as well asthe electric field in each layer (i.e., E_(Si) and E_(ox)) are alsoillustrated.

When an electric field is applied across the waveguide structure by theapplication of a voltage bias to the metal electrodes 210 and 212, theindex of refraction in the waveguide core 220 and the waveguide claddingregions 222 and 224 is altered, through the DC Kerr effect. As describedin relation to FIG. 1, incorporation of an active region (i.e., a phaseadjustment section) as illustrated in FIG. 2 can be utilized toimplement an electro-optic switch.

Because the displacement field perpendicular to the layers (D=κE) mustbe continuous, E_(Si)=(3.9/11.7) E_(ox)=E_(ox)/3.

Thus, a significant portion of the electric field bias applied acrossthe phase adjustment section device is dropped across the silicondioxide cladding regions 222 and 224, which have low-κ values incomparison to the silicon waveguide core, thereby failing to produce thedesired index of refraction change in the silicon waveguide core as thebias is dropped across the low-κ silicon dioxide layers. Given typicalvalues for the waveguide layers designed to operate at 1.55 μm ofd_(Si)=0.5 μm and d_(ox)=0.5 μm, which is approximately the minimumdistance suitable for avoiding optical absorption by the metalelectrodes, the potential drop across the silicon layer for an appliedvoltage bias of V₀ is only V₀/7. Thus, 6/7 of the applied voltage biasis dropped across the silicon oxide layers.

The capacitance of the device schematically illustrated in FIG. 2 perunit area is C/A=1.67/4 πd, in the case where d=d_(ox)=d_(Si) and thelayer capacitances are added in series using cgs units. If the SiO₂ isreplaced with a high-K dielectric the power consumption during operationis reduced significantly. In an embodiment, hafnium dioxide (HfO₂) isutilized in place of the silicon dioxide cladding layers. Assuming atypical dielectric constant for HfO₂ of 39, the potential drop acrossthe silicon waveguide core becomes 5V/8 because, E_(Si)=(39/11.7)E_(ox)=10E_(ox)/3.

The capacitance/area becomes C/A=7.35/4 πd. Thus, replacing the silicondioxide cladding layers with hafnium dioxide cladding layers enablesembodiments of the present invention to lower the applied bias V₀ by afactor of (⅝)/( 1/7)=35/8 while maintaining the same electric field inthe silicon waveguide core, thereby achieving the same switching effect.Power reductions of this sort are of particular benefit to cryogenicelectro-optic switches due to the difficulty in creating high voltagedrivers that operate at low temperatures.

Because the energy per unit area required to charge the capacitance isequal to 0.5CV²/A, replacing the silicon dioxide cladding layers withhafnium dioxide cladding layers reduces the required switching energy bya factor of (1.67/7.35)*(35/8)²=4.4. Thus, embodiments of the presentinvention enable substantial energy savings over conventional designs.One of skill in the art will appreciate that the model discussed inrelation to FIG. 2 is utilized merely to demonstrate the impact ofutilizing high-κ dielectric materials in active devices since actualdevice geometries will not typically achieve benefits associated withthe schematic system illustrated in FIG. 2. There will, however, stillbe significant advantages for typical device designs, including bothcarrier and Kerr based switches, because the high-κ dielectric can beused to force higher electric fields in the lower κ active area of thedevice while reducing or minimizing the overall required energy.

Although the discussion in relation to FIG. 2 has been provided inrelation to the voltage and electric field being applied in the plane ofthe figure, this is not required by the present invention and otherembodiments that are implemented in a “vertical” design are includedwithin the scope of the present invention. Accordingly, the variousmaterials can be formed using epitaxial growth, deposition, layertransfer, or the like to fabricate a structure in which the electricfield is directed from upper layers of the structure to bottom layers orvice versa. One of ordinary skill in the art would recognize manyvariations, modifications, and alternatives.

FIG. 3 is a simplified schematic diagram illustrating adielectric-waveguide-dielectric structure incorporating isotope-enhancedPockels effect materials according to an embodiment of the presentinvention.

Referring to FIG. 3, the cross-section of thedielectric-waveguide-dielectric structure includes an illustration ofsubstrate 310, which supports waveguide layer 320, which includeswaveguide core 340. In some embodiments, substrate 310 is the buriedoxide (BOX) layer of a silicon-on-insulator (SOI) structure, althoughthis is not required by the present invention. Metal contacts 330 and332 are provided to enable application of a voltage bias across siliconwaveguide core 340. Dielectric region 352, dielectric region 354, and/orcladding material 350 disposed adjacent silicon waveguide core 340 canbe fabricated using an isotope-enhanced Pockels effect material, forexample, isotope-enhanced BaTiO₃ (BTO), isotope-enhancedPbZr_(x)Ti_(1-x)O₃ (PZT), isotope-enhanced SrBi₂Nb₂O₉ (SBN),combinations thereof, or the like. In other embodiments, materials thatare characterized by high dielectric constant (κ), for example, hafniumoxide (HfO₂), tantalum oxide (Ta₂O₅), zirconium oxide (ZrO₂), titaniumdioxide (TiO₂), other refractory metal oxides, combinations thereof, orthe like can be utilized as isotope-enhanced dielectric regions,cladding materials, or isotope-enhanced waveguide core materials. Asdescribed more fully herein, BTO, PZT, SBN, and the like can also beused for the waveguide core material in conjunction with a suitablecladding material, for example, a higher refractive index material foran index-guided waveguide or, in some embodiments, a lower indexmaterial for a slot waveguide architecture.

In order to vary the index of refraction in waveguide core 340, avoltage bias is applied using metal contacts 330 and 332, also referredto as electrodes. Since there is no current conduction path in thedielectric-waveguide-dielectric structure, the bias applied to theelectrodes will be dropped across dielectric region 352 between metalcontact 330 and waveguide core 340, waveguide core 340, and dielectricregion 354 between waveguide core 340 and metal contact 332. As will beevident to one of skill in the art, the optical mode present inwaveguide core 340 extends into dielectric regions 352, 354, andcladding material 350, all of which can exhibit the Pockels effectenhanced by isotope substitution. As described herein, embodiments ofthe present invention utilize materials characterized by anisotope-enhanced Pockels effect (which results from a large second ordernon-linear susceptibility, χ⁽²⁾).

As described herein, some embodiments of the present invention utilizewaveguide cladding materials including isotope-enhanced Pockels effectmaterial, also referred to as isotope-enhanced material, whereas inother embodiments, waveguide core 340 can also include isotope-enhancedPockels effect material. Thus, in a first embodiment, waveguide core 340is fabricated using a silicon waveguide material while cladding material350 and/or dielectric regions 352 and 354 are fabricated using anisotope-enhanced Pockels effect material. In a second embodiment,waveguide core 340 is fabricated using an isotope-enhanced Pockelseffect material while cladding material 350 and/or dielectric regions352 and 354 are fabricated using lower index dielectric materials, forexample, silicon oxide or silicon nitride. Moreover, in addition toridge waveguide structures, slot waveguide structures are includedwithin the scope of the present invention.

Applying a bias to metal contacts 330 and 332 (i.e., electrodes) resultsin charging of device capacitance. Typically, this capacitance willscale with the length of the section of waveguide over which therefractive index is being modulated. Charging or discharging thiscapacitance requires an energy of ½ CV², where C is the devicecapacitance and V is the bias applied across the device capacitance.Increasing the strength of the Pockels effect reduces the electric fieldrequired to obtain a desired optical phase shift. This allows one toeither reduce the applied bias or shorten the length of the region towhich it is applied, thereby lowering the device capacitance. Loweringthe bias or decreasing the capacitance reduces the energy required toswitch the state of the device. Decreasing the optical path lengthreduces the optical loss in the device.

The strength of the Pockels effect in a switch or modulator can becharacterized by an effective Pockels coefficient, r_(eff), where thechange in refractive index is given by Δn=r_(eff)E Here, E is theelectric field applied to the active region of the device. Moregenerally, the Pockels effect is described by a third rank tensor withcomponents, r_(ijk). Formally, this tensor is defined by:

${{\Delta\left( \frac{1}{ɛ} \right)}_{ij} = {\sum\limits_{k}{r_{ijk}E_{k}}}},$where ε is the high frequency dielectric tensor and E_(k) refers to thecomponents of the electric field. The effective Pockels coefficient of aswitch, r_(eff), is a weighted average of the tensor components thatdepends on the device geometry and propagating optical mode. The tensorcomponents, in turn, are the sum of contributions from electronic,ionic, and piezoelectric effects. In many cases the ionic contributionr_(ijk) ^(ion), which is given by the equation below, dominates:

$r_{ijk}^{ion} = {\frac{{- 4}\pi}{\sqrt{V}n_{ii}^{2}n_{jj}^{2}}{\sum\limits_{m}\frac{\alpha_{ij}^{m}p_{k}^{m}}{\omega_{m}^{2}}}}$where ω_(m) represent phonon frequencies. As indicated by thisdependence, the Pockels effect is highly dependent on phononfrequencies. In fact, it can be enhanced near phase transitions where‘phonon mode softening’ leads to small phonon frequencies. The frequencyof the phonon modes also depends on the mass of the atoms involved inthe mode. In general, the phonon frequency scales inversely as thesquare root of the mass (Cardona, Rev. of Mod. Phys. 77, 1173 (2005)).Therefore, by replacing atoms in a Pockels material with isotopes of adifferent (i.e., higher) mass, embodiments of the present inventionproduce a strong impact on the Pockels tensor, as well as thetemperatures at which it peaks (i.e., the temperatures at whichstructural phase transitions occur). Accordingly, some embodiments ofthe present invention enhance the Pockels effect (i.e., by enhancing therelevant Pockels tensor components) in films used in optical switches bysubstituting different isotopes for the constituent atomic species withisotopes of higher mass. In other embodiments, isotopes are substitutedsuch that isotopes of a smaller mass are used in the substitution,thereby enhancing the Pockels effect in these embodiments.

Using BTO as an example, the titanium atom at the center of the unitcell is perhaps most important in phonon modes that impact the Pockelstensor. This is because displacement of the titanium atom from thecenter of the BTO unit cell is the primary source of the polarization ofBTO. Titanium has five stable, naturally occurring isotopes (⁴⁶Ti to⁵⁰Ti), with abundances ranging from 5% (⁵⁰Ti) to 74% (⁴⁸Ti). Theseisotopes are commercially available and could be utilized in most thinfilm deposition techniques. Similarly, oxygen has three stable isotopes(¹⁶O to ¹⁸O) and ¹⁸O is readily available commercially and could besubstituted for ¹⁶O in the deposition of BTO or other oxygen containingPockels materials. Moreover, barium has six stable isotopes that couldbe used to alter the Pockels tensor of BTO. One or more of theconstituent atoms in the materials with the desired high Pockels effectcan be substituted with heavier isotopes, for example, ⁵⁰Ti can besubstituted for ⁴⁶Ti as well as one or more of the other naturallyisotopes having lower mass. Thus, the BTO can be fabricated such that⁵⁰Ti is substituted in place of the naturally occurring percentages of⁴⁶Ti, ⁴⁷Ti, ⁴⁸Ti, and ⁴⁹Ti. However, embodiments of the presentinvention are not limited to substitution of a single constituent atomand multiple constituent atoms can be substituted, for example, ⁵⁰Ti inplace of one or more of ⁴⁶Ti, ⁴⁷Ti, ⁴⁸Ti, or ⁴⁹Ti, and ¹⁸O in place of¹⁶O or ¹⁷O, or substitution of all three constituent elements: ⁵⁰Ti inplace of one or more of ⁴⁶Ti, ⁴⁷Ti, ⁴⁸Ti, or ⁴⁹Ti, and ¹⁸O in place of¹⁶O or ¹⁷O, and ¹³⁸Ba in place of one or more of ¹³⁰Ba, ¹³²Ba, ¹³⁴Ba,¹³⁵Ba, ¹³⁶Ba, and/or ¹³⁷Ba. Thus, embodiments of the present inventionutilize substitution of one or more naturally occurring isotopes ofconstituent elements in the fabrication of Pockels materials.

Moreover, in addition to complete substitution of the constituent atoms,partial substitution can also be utilized. The inventors have determinedthat not only the increase in mass resulting from the isotopicsubstitution, for example, the percentage increase in mass resultingfrom the substitution of ¹⁸O in place of ¹⁶O, but the position of theconstituent atom in the crystal structure can impact the enhancement ofthe Pockels effect. One of ordinary skill in the art would recognizemany variations, modifications, and alternatives.

In addition to increasing the Pockels effect, isotopes can be used todecrease the low frequency dielectric constant. The energy utilized toswitch an electro-optic switch can be lowered if the low frequencydielectric constant of the Pockels effect material is reduced becausethe device capacitance varies linearly with dielectric constant. Itshould be noted that in some embodiments, reduction of the dielectricconstant is achieved in conjunction with an increase in the Pockelseffect or a decrease in the Pockels effect less than the decrease in thedielectric constant. Lowering the dielectric constant by isotopesubstitution as described herein can thus be utilized for materials thatare not being utilized to provide the Pockels effect, for example, thecladding material in some embodiments. Like the Pockels tensorcoefficients, the low frequency dielectric constant depends on theinverse square of the phonon frequencies:

$ɛ_{\alpha\beta}^{0} = {ɛ_{\alpha\beta}^{\infty} + {\frac{4\pi e^{2}}{M_{0}V}{\sum\limits_{\lambda}\frac{{\overset{˜}{Z}}_{\lambda\alpha}^{*}{\overset{˜}{Z}}_{\lambda\beta}^{*}}{\omega_{m\lambda}^{2}}}}}$

Therefore, substituting isotopes in a material will tend to drive theeffective Pockels coefficient and the low frequency dielectric constantin the same direction, albeit at different rates. To optimize theswitching energy, some embodiments maximize

$\frac{r_{eff}^{2}}{ɛ}.$Thus, appropriately changing the isotopic masses of the constituentatoms in a film can contribute to the optimization of this figure ofmerit as the ratio

$\frac{r_{eff}^{2}}{ɛ}$is tuned. In some implementations, the effective Pockels coefficient andthe low frequency dielectric constant will scale in a substantiallylinear manner with isotope substitution, resulting in a substantiallylinear increase in the ratio

$\frac{r_{eff}^{2}}{ɛ}$with isotope substitution. Thus, embodiments of the present inventionuse isotopic substitution to increase the effective Pockels coefficientor tune the ratio

$\frac{r_{eff}^{2}}{ɛ}$(e.g., to optimize switching energy). In other embodiments, as mentionedabove, isotopic substitution is utilized to tune the dielectricconstant, for example, in portions of the device in which the Pockelseffect is not used, but a lower dielectric constant provides benefits,for example, with respect to device capacitance in regions substantiallyfree of the optical mode.

As discussed above, the incorporation of the isotope-enhanced claddingmaterial characterized by an isotope-enhanced Pockels effect orisotope-enhanced dielectric constant material will result in anincreased percentage of the electric field being dropped across thewaveguide core, thereby either increasing the index of refraction changeat a given voltage bias or providing a given index of refraction changeat a lower voltage bias.

It should be noted that a “vertical” implementation of thedielectric-waveguide-dielectric structure incorporating isotope-enhancedPockels effect materials illustrated in FIG. 3 is included within thescope of the present invention. Dielectric region 352 and 354, as wellas waveguide core 340 can be formed using epitaxial processes to form avertical implementation that will share common elements with theembodiment illustrated in FIG. 3 and provide benefits of smaller devicegeometry as well as other benefits. One of ordinary skill in the artwould recognize many variations, modifications, and alternatives.

FIG. 4 is a simplified schematic diagram illustrating a p-n diodewaveguide structure incorporating isotope-enhanced cladding materialsaccording to an embodiment of the present invention. Referring to FIG.4, the cross-section of the p-n diode waveguide structure includes anillustration of substrate 410, which supports waveguide layer 420, whichincludes p+ contact region 422, p-type region 424, n-type region 426,and n+ contact region 428. In some embodiments, substrate 410 is theburied oxide (BOX) layer of a silicon-on-insulator (SOI) structure,although this is not required by the present invention. Metal contacts430 and 432 are provided to enable application of a voltage bias acrosssilicon waveguide core 440.

The cladding for the waveguide structure includes first isotope-enhancedcladding material 445 that is disposed above and on either side ofsilicon waveguide core 440 and second cladding material 446 that isdisposed above and on either side of first isotope-enhanced claddingmaterial 445. The first isotope-enhanced cladding material ischaracterized by an isotope-enhanced Pockels effect, for example, aPockels effect that is greater than the Pockels effect associated withthe same material fabricated using constituent materials havingnaturally occurring isotope percentages. As an example, silicon can beutilized as waveguide core material 440 and isotope-enhanced leadzirconate titanate (Pb[Zr_((x))Ti_((1-x))]O₃) (PZT), isotope-enhancedbarium titanate (BaTiO₃ (BTO)), isotope-enhanced strontium bariumniobate ((Sr,Ba)Nb₂O₆), combinations thereof, or the like, can beutilized as first isotope-enhanced cladding material 445.

Although different materials are illustrated for first cladding material445 and second cladding material 446, this is not required by thepresent invention and the same material can be utilized for both thefirst and second cladding layers. As an example, the entire claddingcould be fabricated using isotope-enhanced barium titanate, in whichcase, there would be no distinction between the first cladding materialand the second cladding material. In other embodiments, differentcompositions of the same material could be utilized as the firstcladding material and the second cladding material. Moreover, althoughonly two cladding layers are illustrated in FIG. 4, it will beappreciated that more than two cladding layers could be used, forexample, a thin film of a first isotope-enhanced Pockels effect material(e.g., BTO), a thin film of a second isotope-enhanced Pockels effectmaterial (e.g., PZT) deposited after the first cladding material, Nadditional thin films of subsequent cladding materials, and a blanketcoating of a final cladding material. Moreover, although a single layerof the first cladding material is illustrated in FIG. 4, this single“layer” can be made up of multiple sub-layers of different materials orthe same material. One of ordinary skill in the art would recognize manyvariations, modifications, and alternatives.

Thus, embodiments of the present invention utilize low-loss waveguidestructures that are isotope-enhanced and can be produced using standardsilicon photonics foundry processes.

According to embodiments of the present invention, the thickness offirst cladding material 445 is sufficient to enable sufficient overlapbetween the optical mode and the first cladding material to achieve adesired variation in the effective index of refraction seen by thepropagating waveguide optical mode upon application of an electricfield. As an example, the thickness of first cladding layer 445 canrange from about 10 nm to about 1 μm, for example, between tens ofnanometers and hundreds of nanometers. As a result, the electric fieldlines extending from p-type region 424 to n-type region 426 will pass,not only through waveguide core 440, but through the first claddingmaterial disposed on either side of the waveguide core, as well asthrough at least a portion of the first cladding material disposed abovethe waveguide core. As described herein, the incorporation of claddingmaterial with isotope-enhanced Pockels effect enables increasedvariation in the index of refraction of the waveguide structure for agiven voltage bias and applied electric field or a given variation inthe index of refraction of the waveguide structure for a reduced voltagebias and applied electric field.

FIG. 5 is a simplified schematic diagram illustrating a waveguidestructure incorporating isotope-enhanced Pockels effect materialsaccording to an embodiment of the present invention. The embodimentillustrated in FIG. 5 is similar to that illustrated in FIG. 4, but doesnot utilize a p-n junction in waveguide core 540. Rather, undoped region551 (e.g., undoped silicon) is utilized in waveguide core 540, which isan element of a pin junction structure. Otherwise, the descriptionprovided in relation to FIG. 4 is applicable to the embodimentillustrated in FIG. 5 as appropriate. As illustrated in FIG. 5, firstisotope-enhanced cladding material 445 is characterized by anisotope-enhanced Pockels effect and second cladding material 446 can befabricated using a dielectric such as silicon oxide or silicon nitride.One of ordinary skill in the art would recognize many variations,modifications, and alternatives.

FIG. 6 is a simplified schematic diagram illustrating a p-n diodewaveguide structure incorporating a planar isotope-enhanced layeraccording to an embodiment of the present invention. The structureillustrated in FIG. 6 shares common elements with the structuresillustrated in FIG. 4 and the discussion provided in relation to FIG. 4is applicable to the structure illustrated in FIG. 6 as appropriate.Referring to FIG. 6, the cross-section of the p-n diode waveguidestructure includes an illustration of substrate 610, which supportswaveguide layer 650, which includes p+ contact region 652, p-type region654, n-type region 656, and n+ contact region 658. In some embodiments,substrate 610 is the buried oxide (BOX) layer of a silicon-on-insulator(SOI) structure, although this is not required by the present invention.Metal contacts 660 and 662 are provided to enable application of avoltage bias across the silicon waveguide core 664.

The waveguide core can be formed as a silicon ridge waveguide or othersuitable waveguide structure. After formation of waveguide core 664,which can be a silicon waveguide core, a dielectric layer (e.g., SiO₂)is deposited and subsequently planarized to form a first portion of thewaveguide cladding. As illustrated in FIG. 6, first dielectric region667 and second dielectric region 668 are disposed on either lateral sideof waveguide core 664. After planarization, an isotope-enhanced claddinglayer 661 is formed as a second portion of the waveguide cladding usinga material, in some embodiments, that has been isotopically enhanced asdescribed herein. Isotope-enhanced cladding layer 661 can be depositedusing a deposition process or can be transferred using a layer transferprocess.

Isotope-enhanced cladding layer 661 is characterized by anisotope-enhanced Pockels effect that is greater than the Pockels effectassociated with materials fabricated using constituent materials havingnaturally occurring isotope percentages. As an example, silicon can beutilized as waveguide core material 664, isotope-enhanced BTO can beutilized as isotope-enhanced cladding layer 661, and silicon dioxide(SiO₂) (or silicon nitride (Si₃N₄)) can be used as the material forfirst dielectric region 667 and second dielectric region 668 (i.e., thefirst portion of the waveguide cladding). In alternative embodiments, anisotope-enhanced Pockels material can also be utilized for firstdielectric region 667 and second dielectric region 668. As illustratedin FIG. 6, one or more additional (optional) cladding layers 663 can beformed on the isotope-enhanced cladding layer to provide the desiredoptical confinement. As an example, silicon dioxide (SiO₂) can bedeposited on isotope-enhanced cladding layer 661 to form an additionalcladding layer. The cladding materials can utilize suitable materials asdiscussed in relation to FIG. 4.

Although different materials are illustrated in FIG. 6 for the firstportion of the waveguide cladding and the second portion of thewaveguide cladding, this is not required by the present invention andthe same material can be utilized for both the first portion of thewaveguide cladding and the second portion of the waveguide cladding. Asan example, after formation of the ridge waveguide, isotope-enhanced BTOcould be deposited and planarized to form the first portion of thewaveguide cladding and the second portion of the waveguide cladding.Alternatively, after formation of the ridge waveguide, isotope-enhancedBTO could be deposited and planarized to form the first portion of thewaveguide cladding. Subsequently, a layer transfer process could beutilized to position isotope-enhanced cladding layer 661 above thewaveguide core. The discussion of alternative materials and structuresas described in relation to FIG. 4 is applicable to the embodimentillustrated in FIG. 6 as appropriate. One of ordinary skill in the artwould recognize many variations, modifications, and alternatives.

Because embodiments of the present invention utilize the Pockels effect,the crystal orientation of the electro-optic material can be controlledto align the applied electric field with respect to the crystal axes ofthe Pockels effect material in order to maximize the Pockels effect.Moreover, the polarization of the light propagating in the waveguide canbe aligned with respect to the crystal axes of the isotope-enhancedPockels effect material. Thus, alignment between the crystal axes andthe applied electric field (e.g., at frequencies of gigahertz, forexample, up to 100 GHz or higher, and below, which may be referred to asthe “DC” electric field in contrast with optical frequencies) as well asalignment between the crystal axes and the electric field of the opticalmode (e.g., at optical frequencies) are implemented according to someembodiments of the present invention. Moreover, the orientation of thewaveguide (i.e. the propagation direction of the light) with respect tothe crystallographic axes can also controlled in some embodiments.

For example, as illustrated in FIG. 6, isotope-enhanced claddingmaterial 661 is characterized by crystal axes and the Pockels effect ischaracterized by a tensor. The crystal orientation of theisotope-enhanced cladding material, and the direction of propagation ofthe transmitted light and its polarization direction, can be aligned sothat the largest coefficient of the Pockels tensor is utilized. As aresult, the change in index of refraction produced by the application ofthe applied electric field is maximized. As will be evident to one ofskill in the art, the maximization of these values is not required bythe present invention and embodiments of the present invention includeimplementations in which coefficients of the Pockels effect tensors thatare not the largest coefficients are utilized. These embodiments areincluded within the scope of the present invention.

Moreover, the polarization of the optical mode can be selected to alignthe electric field at optical frequencies with the largest value of thePockels tensor. Referring to FIG. 6, if the polarization of the opticalmode is a transverse electric (TE) mode, the optical electric field ispolarized in the plane of the figure (e.g., along the lateral direction)and perpendicular to the longitudinal direction of the waveguide, whichis normal to the plane of the figure and orthogonal to the lateral andtransverse directions. Thus, the optical electric field and the appliedelectric field are both aligned along the lateral direction in anembodiment. In order to maximize the index of refraction change producedby the applied electric field, the crystal structure of theisotope-enhanced cladding material is aligned as discussed above. As anexample, BTO is characterized by a tetragonal crystal structure. Thus,for BTO, the c-axis is aligned along the lateral direction with thea-axes perpendicular to the lateral direction to achieve the largestPockels effect, for example, by increasing the Pockels tensor componentsr₄₂ and r₅₁, which are equal for BTO.

In some embodiments utilizing materials with non-cubic crystalstructures, the cladding material is formed such that half of thecrystallographic domains are oriented with their c-axis in a firstdirection in-plane direction and half of the domains are oriented in asecond in-plane direction perpendicular to the first direction. Forthese embodiments, for example, in embodiments utilizing BTO, thecladding material can be oriented such that the applied electric fieldand/or the optical electric field polarization are perpendicular to thevector bisecting the first direction and the second direction, i.e.,oriented at 45° to the first direction and the second direction toprovide a component of the applied electric field that utilizes thelargest of the Pockels tensor components. Other materials can beoriented at other angles to enhance the Pockels effect as a function ofthe Pockels tensor characterizing the other materials. Thus, the indexof refraction change due to the applied electric field is maximized byoptimizing the utilization of the largest components of the Pockelseffect tensors. One of ordinary skill in the art would recognize manyvariations, modifications, and alternatives.

Thus, some embodiments of the present invention utilize the electrodegeometry (to define the orientation of the applied electric field), thecrystal orientation of the isotope-enhanced cladding material (to definethe Pockels material tensor alignment), and/or the waveguide geometry(to define the optical electric field polarization and light propagationdirection) to ensure that the optimum index of refraction changeresulting from the Pockels effect is achieved.

FIG. 7 is a simplified schematic diagram illustrating a buried waveguidestructure incorporating a planar isotope-enhanced cladding layeraccording to an embodiment of the present invention. The structureillustrated in FIG. 7 shares common elements with the structuresillustrated in FIGS. 4 and 6 and the discussion provided in relation toFIGS. 4 and 6 is applicable to the structure illustrated in FIG. 7 asappropriate. For purposes of clarity, the conductivity type of thevarious materials is not illustrated in FIG. 7, but materials withdiffering conductivity as illustrated in FIGS. 4 and 6 can be utilizedin the structure illustrated in FIG. 7 as appropriate.

As illustrated in FIG. 7, substrate 710 supports buried waveguide 770,which is illustrated as positioned between first dielectric region 772,which as illustrated in FIG. 7 can be SiO₂, and second dielectric region774, which as illustrated in FIG. 7 can be SiO₂. These first and seconddielectric regions 772 and 774 can be considered as a first portion ofthe waveguide cladding.

Isotope-enhanced cladding layer 775 is formed as a second portion of thewaveguide cladding using a material with an isotope-enhanced Pockelseffect. Isotope-enhanced cladding layer 775 can be deposited using adeposition process or can be transferred using a layer transfer process.

Isotope-enhanced cladding layer 775 is characterized by anisotope-enhanced Pockels effect that is greater than the Pockels effectassociated with materials fabricated using constituent materials havingnaturally occurring isotope percentages. As an example, silicon can beutilized as waveguide core material 770, isotope-enhanced BTO can beutilized as isotope-enhanced cladding layer 775, and silicon dioxide(SiO₂) can be used as the material for first dielectric region 772 andsecond dielectric region 774 (i.e., the first portion of the waveguidecladding). As illustrated in FIG. 7, one or more additional claddinglayers 777 can be formed on the first cladding layer to provide thedesired optical confinement. As an example, silicon dioxide (SiO₂) canbe deposited on isotope-enhanced cladding layer 775 to form additionalcladding layer 777. The cladding materials can utilize suitablematerials as discussed in relation to FIGS. 4 and 6.

In order to establish an applied electric field extending through theisotope-enhanced cladding layer 775 and waveguide core 770, a biasvoltage is applied to electrodes 730 and 732, which can be metalelectrodes or other suitable materials that provide electricalconductivity. In some embodiments, electrical contact is provided to thewaveguide materials, which may include doped regions that form a p-njunction as illustrated in FIG. 4, in order to prevent carrier screeningthat may result from application of the electric field across thewaveguide core.

FIG. 8 is a simplified schematic diagram illustrating a buried waveguidestructure incorporating a planar isotope-enhanced cladding layeraccording to another embodiment of the present invention. The structureillustrated in FIG. 8 shares common elements with the structuresillustrated in FIGS. 4, 6, and 7 and the discussion provided in relationto FIGS. 4, 6, and 7 is applicable to the structure illustrated in FIG.8 as appropriate. For purposes of clarity, the conductivity type of thevarious materials is not illustrated in FIG. 8, but materials withdiffering conductivity as illustrated in FIGS. 4 and 6 can be utilizedin the structure illustrated in FIG. 8 as appropriate. As illustrated inFIG. 8, substrate 810 supports buried waveguide 880, which isillustrated as positioned above a planar isotope-enhanced cladding layer882 and partially surrounded by second cladding layer 884.

Planar isotope-enhanced cladding layer 882 is formed using a materialwith an isotope-enhanced Pockels effect. Planar isotope-enhancedcladding layer 882 can be deposited using a deposition process or can betransferred using a layer transfer process.

Planar isotope-enhanced cladding layer 882 is characterized by anisotope-enhanced Pockels effect that is greater than the Pockels effectassociated with materials fabricated using constituent materials havingnaturally occurring isotope percentages. As an example, silicon can beutilized as the waveguide core material 880, isotope-enhanced BTO can beutilized as planar isotope-enhanced cladding layer 882, and silicondioxide (SiO₂) can be used as the material for second dielectric layer884. The cladding materials can utilize suitable materials as discussedin relation to FIGS. 4, 6, and 7.

In order to establish an applied electric field extending throughisotope-enhanced cladding layer 882 and the waveguide core 880, a biasvoltage is applied to electrodes 830 and 832, which can be metalelectrodes or other suitable materials that provide electricalconductivity. In some embodiments, electrical contact is provided to thewaveguide materials, which may include doped regions that form a p-njunction as illustrated in FIG. 4, in order to prevent carrier screeningthat may result from application of the electric field across thewaveguide core.

FIG. 9 is a simplified schematic diagram illustrating adielectric-waveguide-dielectric structure incorporating isotope-enhancedcladding materials according to an embodiment of the present invention.The dielectric-waveguide-dielectric structure illustrated in FIG. 9shares similarities with the dielectric-waveguide-dielectric waveguidestructure illustrated in FIG. 6 and the discussion provided in relationto FIG. 6 is applicable to FIG. 9 as appropriate.

Referring to FIG. 9, the cross-section of thedielectric-waveguide-dielectric structure includes an illustration ofsubstrate 910, which supports waveguide layer 920, which includeswaveguide core 940. In some embodiments, substrate 910 is the buriedoxide (BOX) layer of a silicon-on-insulator (SOI) structure, althoughthis is not required by the present invention. Metal contacts 930 and932 are provided to enable application of a voltage bias acrosswaveguide core 940, which can be silicon.

The cladding material surrounding waveguide core 940 includes a firstisotope-enhanced cladding layer 922 disposed below the waveguide core,lateral isotope-enhanced cladding layers 924 and 926 disposed on eitherside of the waveguide core, and second isotope-enhanced cladding layer928 disposed above the waveguide core. In addition to firstisotope-enhanced cladding layer 922, lateral isotope-enhanced claddinglayers 924 and 926, and second isotope-enhanced cladding layer 928,proximal dielectric regions 950, 952, and 954 are disposed with one ormore of the lateral isotope-enhanced cladding layers 924 and 926 orsecond isotope-enhanced cladding layer 928 between the proximal thedielectric regions and the waveguide core.

One of more of first isotope-enhanced cladding layer 922, lateralisotope-enhanced cladding layers 924 and 926, and secondisotope-enhanced cladding layer 928 are characterized by anisotope-enhanced Pockels effect that is greater than the Pockels effectassociated with materials fabricated using constituent materials havingnaturally occurring isotope percentages. In some embodiments, theisotope-enhanced Pockels effect material is utilized to form thewaveguide core (e.g., waveguide core 940) and a suitable dielectricmaterial with a lower index of refraction than the waveguide core isutilized as the cladding material.

As an example, silicon can be utilized as the waveguide core 940 andisotope-enhanced BTO can be utilized as first isotope-enhanced claddinglayer 922, lateral isotope-enhanced cladding layers 924 and 926, andsecond isotope-enhanced cladding layer 928, and silicon dioxide (SiO₂)can be used as proximal dielectric regions 950, 952, and 954. Othersuitable materials for first isotope-enhanced cladding layer 922,lateral isotope-enhanced cladding layers 924 and 926, and secondisotope-enhanced cladding layer 928 and/or proximal dielectric regions950, 952, and 954 include isotope-enhanced lead zirconate titanate(Pb[Zr_((x))Ti_((1-x))]O₃) (PZT), isotope-enhanced strontium bariumniobate ((Sr,Ba)Nb₂O₆), combinations thereof, or the like.

Although different materials are illustrated for first isotope-enhancedcladding layer 922, lateral isotope-enhanced cladding layers 924 and926, and second isotope-enhanced cladding layer 928 and proximaldielectric regions 950, 952, and 954, this is not required by thepresent invention and the same material can be utilized for both firstisotope-enhanced cladding layer 922, lateral isotope-enhanced claddinglayers 924 and 926, and second isotope-enhanced cladding layer 928 andproximal dielectric regions 950, 952, and 954. As an example, the entirecladding could be fabricated using isotope-enhanced BTO, in which case,there would be no distinction between first isotope-enhanced claddinglayer 922, lateral isotope-enhanced cladding layers 924 and 926, andsecond isotope-enhanced cladding layer 928 and proximal dielectricregions 950, 952, and 954. In other embodiments, different compositionsof the same material could be utilized as the various claddingmaterials. Moreover, although only two cladding layers are illustratedin FIG. 10, it will be appreciated that more than two cladding layerscould be used, for example, a thin film of a first isotope-enhancedcladding material (e.g., isotope-enhanced BTO), a thin film of a secondisotope-enhanced cladding material (e.g., isotope-enhanced PZT)deposited after the first isotope-enhanced cladding material, Nadditional thin films of subsequent cladding materials, which may or maynot be isotope-enhanced, and a blanket coating of a final claddingmaterial, which may or may not be isotope-enhanced. Moreover, although asingle layer of cladding material is illustrated in FIG. 9 for firstisotope-enhanced cladding layer 922, lateral isotope-enhanced claddinglayers 924 and 926, and second isotope-enhanced cladding layer 928,these single “layers” can be made up of multiple sub-layers of differentmaterials or the same material. One of ordinary skill in the art wouldrecognize many variations, modifications, and alternatives.

It should be noted that a “vertical” implementation of thedielectric-waveguide-dielectric structure incorporating isotope-enhancedPockels effect materials illustrated in FIG. 9 is included within thescope of the present invention. Proximal dielectric region 952 and 954,as well as waveguide core 940 can be formed using epitaxial processes toform a vertical implementation that will share common elements with theembodiment illustrated in FIG. 9 and provide benefits of smaller devicegeometry as well as other benefits. One of ordinary skill in the artwould recognize many variations, modifications, and alternatives.

FIGS. 10A-10C are simplified schematic diagrams illustrating fabricationof an isotope-enhanced semiconductor structure according to anembodiment of the present invention. In FIG. 10A, a handle substrate1010, for example, a silicon handle substrate, supports anisotope-enhanced Pockels effect layer 1012. As an example,isotope-enhanced Pockels effect layer 1012 can be formed as a thin filmof at least one of isotope-enhanced BTO, isotope-enhanced PZT,isotope-enhanced SBN, combinations thereof, or the like. Isotopeenhanced Pockels effect layer 1012 can be fabricated using varioustechniques including deposition and layer transfer processes

FIG. 10B illustrates wafer scale bonding of an isotope-enhancedsemiconductor structure to a substrate structure according to anembodiment of the present invention. In FIG. 10B, isotope-enhancedPockels effect layer 1012 of an isotope-enhanced semiconductor structureincluding handle substrate 1010 is wafer scale bonded to a substratestructure in the form of an SOI substrate with silicon substrate 1020,buried oxide layer 1022, and single crystal silicon layer 1024. In otherembodiments, other substrate structures other than SOI substrates areutilized. FIG. 10C illustrates the isotope-enhanced semiconductorstructure formed following wafer scale bonding. The isotope-enhancedsemiconductor structure includes silicon substrate 1020, buried oxidelayer 1022, single crystal silicon layer 1024, and isotope-enhancedPockels effect layer 1012.

Thus, embodiments of the present invention provide an isotope-enhancedsemiconductor structure that includes a silicon substrate structure andan isotope-enhanced Pockels effect layer coupled to the siliconsubstrate structure. Although isotope-enhanced Pockels effect layer 1012is illustrated as being bonded to single crystal silicon layer 1024 inFIG. 10C, this is not required by the present invention and suitablebuffer layer(s) can be utilized during the wafer scale bonding process.Moreover, although a layer transfer process is illustrated in FIGS.10A-10C, fabrication of the isotope-enhanced semiconductor structure isnot limited to this particular fabrication process and other processes,including deposition and the like are included within the scope of thepresent invention.

It is also understood that the examples and embodiments described hereinare for illustrative purposes only and that various modifications orchanges in light thereof will be suggested to persons skilled in the artand are to be included within the spirit and purview of this applicationand scope of the appended claims.

What is claimed is:
 1. A waveguide structure comprising: a substrate; awaveguide core coupled to the substrate and including a first materialcharacterized by a first index of refraction; and an isotope-enhancedcladding layer at least partially surrounding the waveguide core andincluding a second material characterized by a second index ofrefraction less than the first index of refraction and anisotope-enhanced Pockels effect.
 2. The waveguide structure of claim 1wherein the isotope-enhanced Pockels effect is greater than a Pockelseffect of the second material using constituent materials havingnaturally occurring isotope percentages.
 3. The waveguide structure ofclaim 2 wherein one or more constituent atoms of the isotope-enhancedcladding layer are characterized by an isotope percentage greater than anaturally occurring isotope percentage of the one or more constituentatoms.
 4. The waveguide structure of claim 1 further comprising a secondcladding layer coupled to the isotope-enhanced cladding layer.
 5. Thewaveguide structure of claim 4 wherein the waveguide core comprisessilicon, the isotope-enhanced cladding layer comprises isotope-enhancedbarium titanate and the second cladding layer comprises silicon dioxide.6. The waveguide structure of claim 1 wherein the second material ischaracterized by a χ⁽³⁾ value greater than 2.2×10¹⁸ m²/W.
 7. Thewaveguide structure of claim 1 wherein the second material comprises atleast one of isotope-enhanced barium titanate (BaTiO₃) orisotope-enhanced lead zirconate titanate (PZT).
 8. The waveguidestructure of claim 1 wherein the waveguide structure comprises aMach-Zehnder interferometer.
 9. The waveguide structure of claim 1wherein the waveguide structure comprises a ring resonator.
 10. Anoptical switch structure comprising: a substrate; a waveguide structurecoupled to the substrate; a set of electrodes positioned adjacent thewaveguide structure, wherein the set of electrodes are configured toestablish an applied electric field having a component oriented along alateral direction; wherein the waveguide structure comprises: awaveguide core configured to support a guided mode and propagating alonga longitudinal direction orthogonal to the lateral direction andincluding a first material characterized by a first index of refraction;and an isotope-enhanced waveguide cladding at least partiallysurrounding the waveguide core and including a second materialcharacterized by a second index of refraction less than the first indexof refraction and an isotope-enhanced Pockels effect higher than aPockels effect of the second material with constituent materials havingnaturally occurring isotope percentages.
 11. The optical switchstructure of claim 10 wherein the waveguide core comprises silicon. 12.The optical switch structure of claim 10 wherein the waveguide coreconsists of silicon.
 13. The optical switch structure of claim 10wherein the waveguide core comprises an isotope-enhanced material. 14.The optical switch structure of claim 10 wherein the guided modecomprises a TE polarization mode.
 15. The optical switch structure ofclaim 10 further comprising: a first electric contact and a secondelectrical contact configured to generate an applied electric fieldproduced in the waveguide structure that is characterized by adirection; and the isotope-enhanced waveguide cladding is characterizedby an isotope-enhanced Pockels tensor having a maximum value alignedalong the direction.
 16. The optical switch structure of claim 15wherein a guided mode supported by the waveguide core has a direction ofpolarization aligned with the direction.
 17. A semiconductor structurecomprising: a substrate; and an isotope-enhanced layer including a thinfilm of at least one of isotope-enhanced barium titanate,isotope-enhanced lead zirconate titanate, or isotope-enhanced strontiumbismuth niobate coupled to the substrate.
 18. The semiconductorstructure of claim 17 wherein: the substrate comprises asilicon-on-insulator (SOI) structure including a single crystal siliconlayer bonded to a buried oxide layer; and the isotope-enhanced layer isbonded to the single crystal silicon layer.
 19. The semiconductorstructure of claim 17 further comprising a silicon waveguide opticallycoupled to the isotope-enhanced layer.
 20. The semiconductor structureof claim 17 wherein the isotope-enhanced layer comprises: a waveguidecore coupled to the substrate and including a first materialcharacterized by a first index of refraction and an isotope-enhancedPockels effect greater than a Pockels effect of the first material withconstituent materials having naturally occurring isotope percentages;and a cladding layer at least partially surrounding the waveguide coreand including a second material characterized by a second index ofrefraction less than the first index of refraction.